Covers for glass thermometers are disclosed by Govoni in U.S. Pat. No. 2,768,736. These covers are elongated one piece tubular members having closed ends adapted to fit around the temperature sensing end of the thermometer. The wall of the cover is thin to allow rapid heating and heat transmission so that the thermometer can quickly reach its maximum temperature. Electronic clinical thermometers are equipped with elongated probes having temperature sensing elements. Disposable covers are releasably mounted on the probes so that the thermometer can be used with a number of patients by merely replacing the cover. Examples of this type of probe and cover are shown in U.S. Pat. Nos. 3,738,172 and 3,905,232. Tongret in U.S. Pat. No. 3,254,533 shows a disposable cover having an open end with an inwardly directed flange positioned over a base on the probe. The closed end of the probe has an aluminum tip for rapid transfer of heat to the temperature sensing element of the probe. Oudewaal in U.S. Pat. No. 3,822,593 discloses a disposable cover with a flexible elastic tip. A sleeve structure is used to mount the elastic tip on the end of the elongated tube. The elastic tip is adapted to be stretched over the end of the temperature sensing element of the probe. The tube has outwardly directed projections locatable in a groove in the collar to latch the cover on the probe. Another probe cover is disclosed by Naumann in U.S. Pat. No. 3,880,282. This probe has a one-piece tapered hollow body having a small closed end. The wall thickness at the closed end is thin to allow relatively rapid heat transfer through the material of the closed end.